John Wick, prior to being a hitman, served in the United States Marine
Corps. This can be noticed by the tattoo on his back, which from Latin
to English says "Fortune Favors the Brave", the motto of the United
States Marine Corps, 2nd battalion, 3rd Marines who have been through
5 tours of duty.
Update: Also from the wiki,
According to Wick's Crimefest description, he and Chains were former
comrades during their time in the military.
It is an established fact in the Payday games that John Wick served in the military.
Payday is widely believed to be canon which is evident from many facts including the following
John Wick literally being in the game
"Continental Coins" being used as a form of in game currency used to upgrade the safehouse.
There exists a John Wick weapons purchaseable DLC pack for the game which features the same weapons from the movies.
The creative team has not made any statements regarding this but I suspect it is because the obscurity of John Wick's past is a major factor in the appeal of this movie. However, it is safe to assume that he did serve in the military prior to becoming a hitman.